Although the concept of randomized assignment to control for extraneous factors reaches back hundreds of years, the first empirical use appears to have been in an 1835 trial of homeopathic medicine. Throughout the 19th century, there was primarily a growing awareness of the need for careful comparison groups, albeit often without the realization that randomization could be a particularly clean method to achieve that goal. In the second and more crucial phase of this history, four separate but related disciplines introduced randomized control trials within a few years of one another in the 1920s: agricultural science, clinical medicine, educational psychology, and social policy (specifically political science). Randomized control trials brought more rigor to fields that were in the process of expanding their purviews and focusing more on causal relationships. In the third phase, the 1950s through the 1970s saw a surge of interest in more applied randomized experiments in economics and elsewhere, in the lab and especially in the field.
That is from a Julian C. Jamison paper done at the World Bank, via various people in my Twitter feed.